Volume 15, Issue 5
Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision

Zhenning Cai, Yuwei Fan, Ruo Li & Zhonghua Qiao

Commun. Comput. Phys., 15 (2014), pp. 1368-1406.

Published online: 2014-05

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  • Abstract

We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation, to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization. The numbers of Maxwell boundary condition required for well-posedness are studied. The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed. By solving several benchmark problems, we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.

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@Article{CiCP-15-1368, author = {}, title = {Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {5}, pages = {1368--1406}, abstract = {

We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation, to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization. The numbers of Maxwell boundary condition required for well-posedness are studied. The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed. By solving several benchmark problems, we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.220313.281013a}, url = {http://global-sci.org/intro/article_detail/cicp/7142.html} }
TY - JOUR T1 - Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision JO - Communications in Computational Physics VL - 5 SP - 1368 EP - 1406 PY - 2014 DA - 2014/05 SN - 15 DO - http://doi.org/10.4208/cicp.220313.281013a UR - https://global-sci.org/intro/article_detail/cicp/7142.html KW - AB -

We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation, to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization. The numbers of Maxwell boundary condition required for well-posedness are studied. The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed. By solving several benchmark problems, we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.

Zhenning Cai, Yuwei Fan, Ruo Li & Zhonghua Qiao. (2020). Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision. Communications in Computational Physics. 15 (5). 1368-1406. doi:10.4208/cicp.220313.281013a
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